Rep. Ron Paul hasn’t won a presidential primary or caucus yet, but he is prepared to stay in the Republican race through the party’s convention in August, he said Sunday.

“Right now, we don’t know when the end is, whether it’s going to be May, June, July or August,” the Texas congressman said Sunday in an interview on CNN’s “State of the Union.”

“So I have to assume that it’s going to go into August, because we’re not going to lock it up in May, obviously. So we just have to, you know, wait and see. So that in my mind I anticipate it’s going to go on for a while. And that’s certainly what the supporters want me to do,” he said.

Mr. Paul, who is running last in the delegate count among the four Republican presidential contenders, disagreed with the contention that his campaign had failed to win a single contest so far.

“It all depends on how you define winning,” he said.

“Some of these straw votes are straw votes, and sometimes they get very confused in counting votes. You know, take Iowa, for instance, we think we’re going to have the most delegates out of Iowa. And the same thing probably about Maine,” he told CNN.

Mr. Paul, fresh off a raucous rally in Kansas City the night before, had reason to be optimistic: On Saturday, the Maine Republican Party announced Mr. Paul picked up 83 votes on former Massachusetts Gov. Mitt Romney as Republicans from more than two dozen towns in eastern Maine gathered for caucuses postponed two weeks earlier owing to bad weather.

The extra votes weren’t enough to erase Mr. Romney’s 239-vote lead, but Mr. Paul said momentum was on his side.

“The bottom line is, who is going to get the delegates, and we think we’re doing pretty good,” Mr. Paul said.

“It seems like our momentum is picking up,” he said. “I’m actually shocked at the tremendous turnouts that we’ve had. We’ve been out on the road, and we’ve had eight functions here in the last three days. We’ve had 14,000 people turn out. And the enthusiasm seems to be growing.”

After dismissing former Sen. Rick Santorum of Pennsylvania for “pretending to be a conservative,” Mr. Paul acknowledged that Mr. Romney had at least one advantage over Mr. Santorum and the other remaining Republican candidate, former House Speaker Newt Gingrich.

“He would have a more acceptable management style, but as far as issues go, I’m uncomfortable with all three of them,” he said.

Mr. Paul said he doubted Mr. Santorum — now leading national Republican polls after victories earlier this month in Minnesota, Colorado and Missouri — could win the general election. “His voting record is … atrocious,” he said.

At the Paul rally on Saturday night, the libertarian-leaning candidate stoked a crowd of thousands with the warning that the U.S. is “slipping into a fascist system” in the form of government-business alliances.

On Sunday, he stood by the charge, telling CNN that, “I worry about it a lot, because we have a system of … interventionism. And when interventionists exist, it serves the interests of the power of the special interests. And guess who they are? They are the big banks and the very wealthy corporations, and they get these benefits.”